Regardless of the specific reasons, the underlying issue is that, for whatever reason, Google sees the homepage as a better result to show folks searching for [car battery] than the car battery page.
I'm seeing a slightly higher page authority for the home page (23 vs. 20 for /car-battery which, granted, isn't all that big of a difference). The total link count is quite different, though—the home page has 68, and /car-battery has 22.
Also, it looks like the content on /car-batter is pretty thin, and doesn't seem like it'd be especially helpful for someone shopping for a car battery. The interface on that page is much less intuitive, as well,
I can't be 100% positive, but if I had to guess I'd say that Google is preferentially serving the home page because it's a better-developed page with a stronger link profile. If you'd like the category-specific pages to be ranking instead, I'd suggest creating a better user experience on those pages and attracting some links to them.
Make sense?